An electronic device may have a display such as a liquid crystal display. The display may have an array of display pixels. The array of display pixels may display images for a user in an active area of the display. An inactive area of the display may surround the active area. An opaque masking layer may be provided in the inactive area to block internal components in the electronic device from view. An optical component such as a light-based proximity sensor, ambient light sensor, image sensor, or light-emitting status indicator may be aligned with an opening in the opaque masking layer. A liquid crystal shutter may be provided in the display. The liquid crystal shutter may be controlled by control circuitry in the electronic device. The liquid crystal shutter may be aligned with the opening in the opaque masking layer in the inactive area and with the optical component.